Software for manipulating scales and tunings

• Scala - the de facto standard software for creating, manipulating and analyzing tunings
  • Wikipedia article on Scala
  • instructions for Creating Scala scl files for rank two temperaments
• alt-tuner - a tuning plug-in that does adaptive tunings, on-the-fly retuning, and scale analysis by Kite Giedraitis
• Temperament finder - site by Graham Breed
• Tonescape - Music composition, analysis and educational tool by Joe Monzo
• Fractal Tune Smithy & Bounce Metronome - by Robert Walker
• Scala to TUN and MTS online converter - by MicrotonalSoftware.com

Browser-based tuning tools (JavaScript etc.)

• Interval calculator - a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too
• Animated MOS ring demo
• Hexagonal Keyboard Demo - by Sjoerd Visscher
• edjiruler v0.0.1 - Visualize JI intervals close to equal divisions of whole numbers
• Scale Workshop - Generate tuning files in your browser
• Rank 2 Regular Temperament Generator - generate rank2 regular temperaments
• MOSedo - Moments of Symmetry in equal divisions of the octave calculator
• Harmonic Entropy Calculator - Interactive Harmonic Entropy curves.
• Online H-System Calculators - Hunt Intonation Quality Grade Point Average (IQGPA) Calculator
• Microtonal Software Scale Tree - ET Scale Tree Playground
• Offtonic Microtonal Synth
• Wickisynth - tuning demo synthesizer with Wicki-Hayden key layout
• Online 19-edo keyboard
• Online Terpstra keyboard (isomorphic hexagonal keyboard)
• Microtone - A HTML5 uniform keyboard demo with any equal temperament
• The Monochord - Try out just intervals from a base frequency.
• Rational Keyboard - JI keyboard with keys that grow in size
• Tonespiral - Listen to harmonics visualized as a spiral
• Wolfram Alpha Regular Temperament Widgets
• Just Intonation -> EDO calculator

Useful tools for math in general

• Cents to Ratio Calculator - and much more! Also, another one with extensive instructions.
• Fraction Expression Calculator - easily do ratio arithmetic
• Continued Fraction Calculator
• Fast Decimal to Fraction Approximations
• Least Common Denominator of Fractions (LCD) Calculator - put your JI ratios in here!
• Octave - a free, open source equivalent to MATLAB; useful for working with matrices and much more
• Wolfram Alpha - perform a variety of intensive mathematical calculations in your browser
• Online LaTeX Equation Editor - create mathematical expressions in LaTeX format for wiki pages etc.